Alpha Decay

Q. The Q value of a nuclear reaction A + b → C + d is defined by Q = [ mA + mb – mC – md ]c 2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 1 3 2 2 1 1 1 1 H+ H H+ H → (ii) 12 12 20 4 6 6 10 2 C+ C Ne+ He → Atomic masses are given to be m ( 2 1 H ) = 2.014102 u m ( 3 1 H ) = 3.016049 u m ( 12 6 C ) = 12.000000 u m ( 20 10 Ne ) = 19.992439 u

Q. The half-life of $U^{238}$ for $\alpha$-decay is $4.5\times {10}^9\text{years}$. The number of disintegrations per second that occur in $1\text{g}$ of $U^{238}$ is :
(Avogadro number $=6.023\times {10}^{23}{\text{mo1}}^{-1}$)

1. $1.725\times {10}^4{\text{s}}^{-1}$
2. $1.535\times {10}^4{\text{s}}^{-1}$
3. $1.035\times {10}^4{\text{s}}^{-1}$
4. $1.235\times {10}^4{\text{s}}^{-1}$

Q. The rate of decay $\left(R\right)$ of nuclei in a radioactive sample is plotted against time $\left(t\right)$. Which of the following best represents the resulting curve?

1. 
2. 
3. 
4. 

Q.

Hydrogen bomb is based on the principle of

1. Nuclear fission

2. Nuclear fusion

3. Nuclear explosion

4. Chemical reaction

Q.

Why is binding energy important?

Q. The atomic mass of uranium ${}_{92}{\text{U}}^{238}$ is $238.0508u$, that of thorium ${}_{90}{\text{Th}}^{234}$ is $234.0436u$ and that of an alpha particle ${}_2{\text{He}}^4$ is $4.0026u$. Determine the energy released when $\alpha -\text{decay}$ converts ${}_{92}{\text{U}}^{238}$ into ${}_{90}{\text{Th}}^{234}$. $[1u\times c^2=931.5\text{MeV}]$

1. $1.1\text{MeV}$
2. $4.3\text{MeV}$
3. $8.2\text{MeV}$
4. $15.9\text{MeV}$

Q. A radioactive nuclide is produced at the constant rate of $n$ per second. It decays into a stable nucleus with decay constant $\lambda$. If $N_0$ is a number of nuclei at $t=0$, then expected number $N$ of nuclei in existence after $t$ seconds is given by

1. $N=\frac{n}{\lambda }+N_0{e}^{-\lambda t}$
2. $N=N_0{e}^{-\lambda t}$
3. $N=\frac{n}{\lambda }+(N_0+\frac{n}{\lambda })e^{-\lambda t}$
4. $N=\frac{n}{\lambda }+(N_0-\frac{n}{\lambda })e^{-\lambda t}$

Q. Three charges $-Q,q$ and $-3Q$ are arranged as shown in figure. The system of charges will have positive configuration energy if

1. $q<\frac{3Q}{8}$
2. $q>\frac{3Q}{2}$
3. $q<\frac{8Q}{3}$
4. $q>\frac{3Q}{8}$

Q. Let $m_p$ be the mass of a proton, $m_n$ the mass of a neutron, $M_1$ is the mass of a ${}_{10}^{20}\text{Ne}$ nucleus & $M_2$ is the mass of a ${}_{20}^{40}\text{Ca}$ nucleus. Then

1. $M_2=2M_1$
2. $M_2>2M_1$
3. $M_2<M_1+10(m_p+m_n)$
4. $M_1<10(m_n+m_p)$

Q. In an alpha decay the mass number of an element decreases by __.

Q. A nucleus $X^{220}$ at rest decays by emitting an $\alpha$ particle. If energy of the daughter nucleus is $0.2\text{MeV}$, then the $Q$ value of the reaction is

1. $10.8\text{MeV}$
2. $10.9\text{MeV}$
3. $11\text{MeV}$
4. $11.1\text{MeV}$

Q. A radioactive sample undergoes decay as per the following graph. Dotted line represents the slope of the curve at t = 0. If this dotted line intersects the time axis at t = T, choose the correct alternative (Given $t_{\frac{1}{2}}=$half life, $t_{avg}=$ mean life)

1. $t_{\frac{1}{2}}>T$
2. $t_{avg}=T$
3. $t_{\frac{1}{2}}=T$
4. $t_{avg}>T$

Q. Q value of a nuclear reaction is positive. The reaction is (1) Exothermic (2) Endothermic (3) Elastic (4) Both exothermic and endothermic Also explain the concept of Q-value

Q. Two radioactive nuclei A and B decay into C with decay constant $\lambda$ and $2\lambda$ respectively. Initially, both A and B have the same number of nuclei $N_0$. The rate of production of C after time $\frac{\tau }{\lambda }$ is $\alpha \lambda N_0$, where $\tau$ is the half life of A. Find $\alpha$.

Q. Find the amount of energy released in $\text{kWh}$ when $1\text{g}$ of Uranium atoms ${}_{92}{U}^{235}(235.0439$ $\text{amu})$ undergoes fission by slow neutron $\left(1.0087\text{amu}\right)$ and is split into Krypton ${}_{36}K{r}^{92}\left(91.8973\text{amu}\right)$ and Barium ${}_{56}B{r}^{141}\left(140.9139\text{amu}\right)$ (assuming no energy is lost).
$[1\text{amu}{c}^2=931.5\text{MeV}]$.

1. $2.28\times {10}^4$
2. $6.3\times {10}^5$
3. $3\times {10}^6$
4. $1.8\times 0^5$

Q. The mass of a nucleus ${}_Z^{A}X$ is less than the sum of the masses of $(A-Z)$ number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass $M$ can break into two light nuclei of masses $m_1$ and $m_2$ only if $(m_1+m_2)<M.$ Also two light nuclei of masses $m_3$ and $m_4$ can undergo complete fusion and form a heavy nucleus of mass $M^{\prime }$ only if $(m_3+m_4)>M^{\prime }$. The masses of some neutral atoms are given in the table below:

$\begin{array}{cccc}{}_1^{1}H& 1.007825u& {}_1^{2}H& 2.014102u\\ {}_3^{6}Li& 6.015123u& {}_3^{7}Li& 7.016004u\\ {}_{64}^{152}Gd& 151.919803u& {}_{82}^{206}Pb& 205.974455u\\ {}_1^{3}H& 3.016050u& {}_1^{4}He& 4.002603u\\ {}_{30}^{70}Zn& 69.925325u& {}_{34}^{82}Se& 81.916709u\\ {}_{83}^{209}Bi& 208.980388u& {}_{84}^{210}Po& 209.982876u\end{array}$
$(1u=932\frac{MeV}{c^2})$

Q.

A neutron having kinetic energy 12.5 eV collides with a hydrogen atom at rest. Neglect the difference in mass between the neutron and the hydrogen atom and assume that the neutron does not leave its line of motion. Find the possible kinetic energies of the neutron after the event.

Q. 27.A radioactive substance decay 10% in 5days . How much percentage decay in 20 days ?

Q. Find the Q-value and the kinetic energy of the emitted α-particle inthe α-decay of (a) 22688 Ra and (b) 22086 Rn .Given m ( 22688 Ra ) = 226.02540 u, m ( 22286 Rn ) = 222.01750 u, m ( 22286 Rn ) = 220.01137 u, m ( 21684 Po ) = 216.00189 u.

Q.

${}_{83}^{212}$ Bi can disintegrate either by emitting an $\alpha$ -particle or
by emitting a ${\beta }^{-}$ -particle. (a) Write the two equations showing the products of the decays. (b) The probabilities of disintegration by $\alpha$ - and $\beta$ -decays are in the ratio $\frac{7}{13}$. The overall half-life of ${}^{212}$ Bi is one hour. If 1 g of pure ${}^{212}$ Bi is taken at 12.00 noon, what will be the composition of this sample at 1 p.m. the same day?

Q. An energy of $24.6\text{eV}$ is required to remove one of the electron from the ground state of a neutral helium atom. The energy $\left(\text{in eV}\right)$ required to remove both the electrons from the ground state of a neutral helium atom is:

1. $79.0\text{eV}$
2. $51.8\text{eV}$
3. $49.2\text{eV}$
4. $38.2\text{eV}$

Q. Two elements $\text{A}$ and $\text{B}$ with atomic numbers $Z_A$ and $Z_B$ are used to produce characteristic $\text{X}$-rays with frequencies ${\nu }_A$ and ${\nu }_B$ respectively. If $Z_A:Z_B=1:2$, then ${\nu }_A:{\nu }_B$ will be

1. $1:\sqrt{2}$
2. $1:8$
3. $4:1$
4. $1:4$

Q. A nucleus of mass number 220 decays by $\alpha$ - decay. The energy released in the reaction is 5eV. The kinetic energy of an $\alpha$ -particle is

1. $\frac{1}{54}MeV$
2. $\frac{54}{11}MeV$
3. $\frac{55}{54}MeV$
4. $\frac{27}{11}MeV$

Q.

Deffrentiate alpha decay, gamma decay, beta decay

Q.

A radioactive nucleus is being produced at a constant rate α per second. Its decay constant is λ If N0are the
number of nuclei at time t = 0, then maximum number of nuclei possible are

Q. A sample of radioactive material $A$, that has an activity of $10\text{mCi}$ $(1\text{Ci}=3.7\times {10}^{10})\text{decays/s}$, has twice the number of nuclei as another sample of a different radioactive material $B$ which has an activity of $20\text{mCi}$. The correct choices for half-lives of $A$ and $B$ would then be respectively:

1. $10\text{days and}40\text{days}$
2. $5\text{days and}10\text{days}$
3. $20\text{days and}5\text{days}$
4. $20\text{days and}10\text{days}$

Q. Write nuclear reaction equations for(i) α-decay of 22688 Ra (ii) α-decay of 24294 Pu(iii) β–-decay of 3215 P (iv) β–-decay of 21083 Bi(v) β+-decay of 116 C (vi) β+-decay of 9743 Tc(vii) Electron capture of 12054 Xe

Q. Three-fourth of the active nuclei present in a radioactive sample decay in $\frac{3}{4}\text{s}$. The half-life of the sample is

1. $\frac{3}{8}\text{s}$
2. $\frac{3}{4}\text{s}$
3. $\frac{1}{2}\text{s}$
4. $1\text{s}$

Q.

The number of silicon atoms per m³ is 5 × 10²⁸. This is doped simultaneously with 5 × 10²² atoms per m³ of Arsenic and 5 × 10²⁰ per m³ atoms of Indium. Calculate the number of electrons and holes. Given that n_i= 1.5 × 10¹⁶ m⁻³. Is the material n-type or p-type?

Q.

What is binding energy?